Many materials contain small regions of mobile species confined to leaky compartments. Often the average spatial characteristics of such compartments are more interesting than their absolute spatial locations, but frequently the compartments are of a size that is difficult, or impossible, to study by NMR imaging. NMR methods may still be desirable, however, due to the wide range of relatively simple chemical selectivity offered. As discussed below, the present invention provides a method for characterizing local geometries based on spin transport inside and through leaky compartments as detected by pulsed-gradient spin-echo NMR experiments.
Pulsed-gradient spin-echo measurements are well-known methods of measuring molecular transport along one direction. A conventional pulse-gradient spin-echo experiment measures, using an observed echo magnetization, the convolution of the initial spin density with the conditional probability of molecular transport to a new position. Such an experiment is only sensitive to molecular transport along the direction of the applied magnetic field gradient.
More precisely, the observed echo magnetization, S(g), has the form EQU S(g)=.intg.p(r.sub.o).intg.P(r.sub.o /r,t.sub.d) exp {i.gamma.t.sub.e g.(r-r.sub.o)}dr dr.sub.o ( 1)
where p(r.sub.o).rho.initial concentration as a function of the initial position, r.sub.o, P(r.sub.o /r,t.sub.d).rho.conditional probability that a spin initially at r.sub.o will diffuse to r after time t.sub.d, .gamma. is the magnetogyric ratio, and g.gamma.magnetic field gradient strength.
A displacement profile, I(x), is obtained by taking a fourier transform of S(g) with respect to the gradient strength: EQU I(x)=.intg.p(r.sub.o)P(r.sub.o /(r.sub.o +X),t.sub.d) dr. (2)
Thus, I(x) represents a measure of the number of spins which have moved a given amount, x, during t.sub.d.
For an oriented sample, the gradient direction, x, can be varied in separate experiments to measure the bulk anisotropy of molecular mobility within the sample. However, for an un-oriented sample the bulk anisotropy of molecular mobility cannot be measured by this technique.
The pulsed-gradient spin-echo technique of the prior art provides a method for measuring the self-diffusion constant of mobile molecules, as well as the extent of molecular mobility where molecules are confined to impenetrable compartments. For a sample which is composed of compartments which have a uniform size, shape and orientation, the prior art method provides a measurement of the eccentricities of the compartments by comparing the extent of molecular transport along two orthogonal directions. However, in the absence of bulk orientation of the compartments within the sample, this measurement fails since, for randomly oriented compartments, a bulk measurement of the extent of molecular 13 transport is independent of direction.
An example of a patented method using a pulsed-gradient spin-diffusion technique is disclosed in U.S. Pat. No. 4,780,674 (Breton et al).